Motivation

The intensity and sporadic character of acts of political violence interrupts the stability of human development.

Krug et al. (2002) documents the many health and societal effects of individual and collective violence.

UN75-Office (2021) places a high priority in reducing conflict in Eastern and South-eastern Asia, Northern Africa and Western Asia, and, especially Sub-Saharan Africa.

The 2010 global burden of disease report by Rafael Lozano (2012) documents the strong, rippling effect of violence on years of life lost, especially in tropical countries, most notably Sub-Saharan Africa.

Sub-Saharan security tracker(CFR.org)

Technical issues

Richardson (1944), updated by Clauset (2020), dissected inter-state conflict using the Poisson distribution for incidences of war and a power law distribution for severity, measured in battle dead.

Juan Camilo Bohorquez (2009) explains high-frequency, intra-conflict behavior across human insurgencies, again with power law dynamics, outfitted with epoch detection of some major switch points in human behavior.

• The use of power laws and their relaively thick distributional tails highlights the stylized fact of sporadic and intense acts of violence.

Development

Merrill and Orlando (2020) finds that oil producing nations actually increase production, thus increase external payments, with rising political violence.

Bandyopadhyay, Sandler, and Younas (2013) show that political violence depresses foreign direct investment, an engine of development, which can be mitigated by bilateral aid.

Marc Helbling (2020) find that a greater exposure to transnational terrorism is associated with stricter migration controls.

Tobias Böhmelt (2020) provide evidence for the weakening of terrorism diffusion cross borders when host and migrant cultures diverge.

None of these studies employ the modeling of political violence with power law distributions.

Some Questions

1. What is the probable range of incidents of political violence within and across countries?

2. What is the relationship between incidents and casualties?

3. What is the average time to an outbreak of violent incidents?

4. How large a burst can we expect?

5. What is the impact of political violence on social and economic well being?

Data

• The Global Terrorism Data Base (GTD). Over 191,000 events of political violence by country, region, province, and city, from 1970 through 2018 by day, month, and year. The GTD further categorizes the number killed and wounded by type of attack, targets of attack, perpetrators, and mode of operation, for example, insurgency and civil war.

• Life expectancy. Definition: Number of years a newborn infant could expect to live if prevailing patterns of age-specific mortality rates at the time of birth stay the same throughout the infant’s life. Source: UNDESA (2019a). World Population Prospects: The 2019 Revision. Rev 1. New York.. Accessed 30 April 2020.

• Education. Definition: Average number of years of education received by people ages 25 and older, converted from education attainment levels using official durations of each level.
  Source: UNESCO Institute for Statistics (2020), Barro and Lee (2018), ICF Macro Demographic and Health Surveys, UNICEF Multiple Indicator Cluster Surveys and OECD (2019b).

• Gross Domestic Product per capita. Definition: GDP in a particular period divided by the total population in the same period. Source: World Bank (2020a). World Development Indicators database. Washington, DC. Accessed 22 July 2020.

• Foreign Direct Investment. Definition: Sum of equity capital, reinvestment of earnings, other longterm capital and short-term capital, expressed as a percentage of GDP. Source: World Bank (2020a). World Development Indicators database. Washington, DC.. Accessed 22 July 2020.

This study: sub-Saharan Africa countries from 1990 through 2018.

Contiguous geographically, exhibit varying degrees of violence, and inhabit areas of recent high demand for natural resources, that is, Cameroon, Niger, and Nigeria.

Outbreaks

Scaled by casualties

The subset

Desiderata

• The time between events and the number of events it takes to produce an outbreak of violence are among the more policy prone queries.

• The GPD is a mixture of two distributions, a compound of gamma distributed exponential parameters. We can thus express political violence \(V\) as an exponential random variable, with a Gamma distributed rate parameter.

\[ \begin{align} V|\Lambda &\sim \operatorname{Exp}(\Lambda ) \\ \Lambda &\sim \operatorname{Gamma}(\alpha , \, \beta ) \end{align} \]

• Then \(V \sim \operatorname{GPD}(\xi =1/\alpha ,\ \sigma =\beta /\alpha )\).

\[ \begin{align} F'(x) &= f(x) \\ &= \operatorname{Pr}(x \mid \mu, \sigma, \xi) = \frac{1}{\sigma}\left(1 + \xi \left(\frac{x-\mu}{\sigma}\right) \right)_{+}^{- (1+ \xi )/ \xi} \end{align} \]

GPD and Gamma

The Gamma in the Generalized Pareto Distribution

Questions

1. What is the probable range of incidents of political violence within and across countries?

2. What is the relationship between incidents and casualties?

3. What is the average time to an outbreak of violent incidents?

4. How large a burst can we expect?

\(C \rightarrow U \rightarrow V\)

\[ \begin{align} V_i &\sim \operatorname{GPD}( \xi_i, \sigma_i ) \\ \xi_i &= \alpha_i\\ \alpha_i &\sim \operatorname{Normal}( 0,\, 1 ) \\ \sigma_i &\sim \operatorname{Exponential}( 1 ) \end{align} \]

• Here \(V\) are annual counts of those persons killed and wounded and \(i=1\ldots 3\) for each of the countries Cameroon, Niger, and Nigeria.

Casualty power law

Outbreaks

Life expected

Life mediating

\[ \begin{align} G &\sim \operatorname{Normal}( \mu_G, \sigma_G ) \\ \mu_G &= a_G + b_{GL}L \\ L &\sim \operatorname{Normal}( \mu_L, \sigma_L ) \\ \mu_L &= a_L + b_{LV}V \\ V &\sim \operatorname{Gamma-Poisson}( \lambda, \phi ) \\ \operatorname{log}(\lambda) &= a_V + \tau U \\ U &\sim \operatorname{Normal}( 0,\, 1 ) \\ a_G,\,a_L,\,a_V &\sim \operatorname{Normal}( 0,\, 1 ) \\ b_{GL},\, b_{GV}, \, b_{LG}, \, b_{LV}, \, \tau &\sim \operatorname{Normal}( 0,\, 1 ) \\ \sigma_G, \sigma_L, \phi &\sim \operatorname{Exponential}( 1 ) \end{align} \]

• Unobserved factors drive violence

• Violence disrupts life

• Life mediates impact of violence on economic well-being

Disruption of life

Interaction

\[ \begin{align} G &\sim \operatorname{Normal}( \mu_G, \sigma_G ) \\ \mu_G &= a_G + b_{GL}L \\ L &\sim \operatorname{Normal}( \mu_L, \sigma_L ) \\ \mu_L &= a_L + b_{LG}G + b_{LV}V \\ V &\sim \operatorname{Gamma-Poisson}( \lambda, \phi ) \\ \operatorname{log}(\lambda) &= a_V + \tau U \\ U &\sim \operatorname{Normal}( 0,\, 1 ) \\ a_G,\,a_L,\,a_V &\sim \operatorname{Normal}( 0,\, 1 ) \\ b_{GL},\, b_{GV}, \, b_{LG}, \, b_{LV}, \, \tau &\sim \operatorname{Normal}( 0,\, 1 ) \\ \sigma_G, \sigma_L, \phi &\sim \operatorname{Exponential}( 1 ) \end{align} \]

Causal paths

Interactive violence

GDP-Life

Model Selection

PSIS-LOO (Pareto Smoothing Importance Sampling and Leave-One-Out Cross Validation)

          PSIS       SE     dPSIS       dSE    pPSIS    weight
m2.1 -22.49646 8.274647 0.0000000        NA 3.403578 0.5444638
m2.2 -22.13980 8.344651 0.3566525 0.1321547 3.692886 0.4555362

WAIC (Watanable-Aikike or Widely Available Information Criterion)

          WAIC       SE     dWAIC      dSE    pWAIC    weight
m2.1 -22.54389 8.200445 0.0000000       NA 3.379862 0.5424648
m2.2 -22.20335 8.267779 0.3405389 0.128227 3.661114 0.4575352

• Nearly identical results for predictive power

• Life mediation has slightly less information leakage than full interactive model

• Straight out of McElreath (2020)

Note

PSIS exploits the distribution of potentially outlying and influential observations using the GPD to model and measure the data point-wise with the shape parameter \(k=\xi\). Any point with \(k>0.5\) will have infinite variance and thus contribute to a concentration of points – the thick tail.

WAIC is the log-posterior-predictive density (lppd, that is, the Bayesian deviance) and a penalty proportional to the variance in posterior predictions:

\[ WAIC(y, \Theta) = −2(lppd − \underbrace{\Sigma_i var_{\theta}\,log \,\,p(y_i|\theta))}_{penalty} \]

The penalty is related to the number of free parameters in the simulations.

Outliers?

Some results

• The interaction of development measures that impounds the influence of political violence.

• Reporting of violent incidents which result in persons killed or wounded exhibit varying ranges of uncertainty. These ranges vary widely among state actors.

• It appears that GDP per capita is not causative of years of life expected.

• On the contrary, country specific violence causes changes in GDP per capita by way of its more or less obvious influence on years of life expected.

• Longer life strongly impacts GDP per capita and seems to be one channel through which violence is transmitted to economic well-being.

Caveats

• the highly aggregated measurement of all variates. This is unavoidable for years of life expected and GDP per capita. These measures are reported only annually and nationally, which leads to another caveat.

• The nation-state might not be an appropriate model for many of the sub-Saharan countries. Rather a more disaggregated approach may be more yielding of relationships among social and economic development and disruptions to well-being fomented by political violence.

• Violence is reported by latitude and longitude on a daily frequency. Developing a daily model of political violence, and if that is too noisy perhaps a weekly or monthly version, and then aggregating the salient features of violence into aggregated economic and social measures may prove a fruitful avenue of research.

• Aggregate measures such as GDP fail to take into account externalities such as environmental and social costs, including the impact of intense and sporadic violence on generations of persons.

• Disproportionate focus on production and domestic consumption to the detriment of valuing such goals as good governance, equity, environmental conservancy, and stability all summed up in a human good of order.

Statistical models

• We use the generative stochastic models described above as Bayesian statistical models (McElreath (2020))

• Coded in Stan (Carpenter (2017); Team (2020b)) and fit using R (R Core Team) and rstan (Team (2020a)).

• The complete workflow will be maintained on GitHub at https://github.com/wgfoote/developmentandviolence.